Robust State-Feedback Controllability of Linear Systems to a Hyperplane in a Class of Bounded Controls

The paper deals with a linear time-dependent dynamic system with scalar control and input uncertainty (disturbance). Two admissible classes of input uncertainty realizations are considered: the class of measurable bounded functions and the class of measurable quadratically integrable functions. The problem to be studied is the existence of a state feedback control with measurable bounded time realizations transferring the system to a given hyperplane (a target set) from any initial position in a prescribed time for any admissible input uncertainty realization. Necessary and sufficient conditions for the existence of such a control are derived, based on the explicit construction of this control by using an auxilary zero-sum linear-quadratic differential game with a cheap control for the minimizing player. Examples illustrting the theoritical results are presented.